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As several other folks have mentioned, George Gilder has written a new anti-evolution article which was published in the National Review.

There's a lot to hate in this article. It's a poorly written screed, which manages to mix together all of Gilder's bogeymen: feminists, liberals, anti-supply-siders, peer reviewers, academics, and whoever else dares to disagree with him about, well, anything.

Plenty of folks are writing about the problems in this article; as usual, I'm going to ignore most of it, and focus specifically on the mathematical parts of it. Given that his argument is mathematical at root, those errors are fatal to the argument of the article as a whole.

We start with a really strange characterization of Shannon information theory:

After Wealth & Poverty, my work focused on the subject of human creativity as epitomized by science and technology and embodied in computers and communications. At the forefront of this field is a discipline called information theory. Largely invented in 1948 by Claude Shannon of MIT, it rigorously explained digital computation and transmission by zero-one, or off-on, codes called "bits." Shannon defined information as unexpected bits, or "news," and calculated its passage over a "channel" by elaborate logarithmic rules. That channel could be a wire or another other path across a distance of space, or it could be a transfer of information across a span of time, as in evolution.

What's weird about this characterization is that there's a very strange shift in it. He starts off OK: "the channel could be a wire or another path across a distance of space". Where he gets strange is when he drops the channel as he transitions from talking about transmitting information across space to transmitting information across time. Space versus time is not something that we talk about in Shannon's information theory. Information is something abstract; it can be transferred over a channel. What "transferred" means is that the information originated at entity A; and after communication, that information has been seen by entity B. Space, time - they don't make a difference. Gilder doesn't get that.

Crucial in information theory was the separation of content from conduit -- information from the vehicle that transports it. It takes a low-entropy (predictable) carrier to bear high-entropy (unpredictable) messages. A blank sheet of paper is a better vessel for a new message than one already covered with writing. In my book Telecosm (2000), I showed that the most predictable available information carriers were the regular waves of the electromagnetic spectrum and prophesied that all digital information would ultimately flow over it in some way. Whether across time (evolution) or across space (communication), information could not be borne by chemical processes alone, because these processes merged or blended the medium and the message, leaving the data illegible at the other end.

There's a technical term for this kind of writing. We call it "bullshit". He's trying to handwave his way past the facts that disagree with him.

If you want to talk about information carried by a medium, that's fine. But his arguments about "information can not be borne by chemical processes alone?" Gibberish.

DNA is a chemical that makes a rather nice communication channel. It's got a common stable substrate on which you can superimpose any message you want - any information, any length. It's an absolutely wonderful example of a medium for carrying information. But he can't admit that; he can't even really discuss it in detail, because it would blow his argument out of the water. Thus the handwaving "chemical processes can't do it", with absolutely no real argument for why a chemical process "merges the medium and the message".

For another example of how this argument fails: consider a CD/RW drive in a computer. The medium is a piece of plastic with magnetic materials in it. The message is patterns of polarization of those materials. To "record" information on it, you heat it up, and you modify the medium itself by changing the polarization of the particles at a point.

Or best of all: take electromagnetic waves, his example of the "very best" communication medium. It's a waveform, where we superimpose our signal on the wave - the wave isn't like a piece of paper where we've stuck ink to its surface: we force it to carry information by changing the wave itself. The basic frequency of the wave, the carrier, is not modified, but the wave amplitudes are modified - it's not just a simple wave anymore, we've combined the signal and the medium into something different.

What's the difference between that and DNA? You can look at DNA as a long chain of sockets. Each socket must be filled with one of 4 different letters. When we "write" information onto DNA, we're filling those sockets. We've changed the DNA by filling the sockets; but just like the case of radio waves, there's a basic carrier (the underlying chain/carrier wave), and a signal coded onto it (the letters/wave amplitudes).

From this, he tries to go further, and start mixing in some computation theory, building on his lack of comprehension of information theory.

I came to see that the computer offers an insuperable obstacle to Darwinian materialism. In a computer, as information theory shows, the content is manifestly independent of its material substrate. No possible knowledge of the computer's materials can yield any information whatsoever about the actual content of its computations.

This is manifestly not true. In fact, there was a fascinating piece of work a few years ago where people were able to decode the cryptographic system used by a smartcard by using a combination of knowledge of its physical structure, and monitoring its power consumption. From these two things, they were able to backtrack to determine exactly what it was doing, and backtrack to stealing a supposedly inaccessible password.

The failure of purely physical theories to describe or explain information reflects Shannon's concept of entropy and his measure of "news." Information is defined by its independence from physical determination: If it is determined, it is predictable and thus by definition not information. Yet Darwinian science seemed to be reducing all nature to material causes.

Again, gibberish, on many levels.

Shannon's theory does not define information by its "independence from physical determination". In fact, the best "information generators" that we know about are purely physical: radioactive decay and various quantum phenomena are the very best sources we've discovered so far for generating high-entropy information.

And even the most predictable, deterministic process produces information. It may be a small amount of information - deterministic processes are generally low-entropy wrt to information - but they do generate information.

And then, he proceeds to shoot himself in the foot. He's insisted that chemical processes can't be information carriers. But now he asserts that DNA is an information carrier in his sense:

Biologists commonly blur the information into the slippery synecdoche of DNA, a material molecule, and imply that life is biochemistry rather than information processing. But even here, the deoxyribonucleic acid that bears the word is not itself the word. Like a sheet of paper or a computer memory chip, DNA bears messages but its chemistry is irrelevant to its content. The alphabet's nucleotide "bases" form "words" without help from their bonds with the helical sugar-phosphate backbone that frames them. The genetic words are no more dictated by the chemistry of their frame than the words in Scrabble are determined by the chemistry of their wooden racks or by the force of gravity that holds them.

Yup, He says earlier "information could not be borne by chemical processes alone, because these processes merged or blended the medium and the message, leaving the data illegible at the other end." And here he describes how DNA can carry information using nothing but a chemical process. Ooops.

And he keeps on babbling. Next he moves on to "irreducible complexity", and even tries to use Chaitin as a support:

Mathematician Gregory Chaitin, however, has shown that biology is irreducibly complex in a more fundamental way: Physical and chemical laws contain hugely less information than biological phenomena. Chaitin's algorithmic information theory demonstrates not that particular biological devices are irreducibly complex but that all biology as a field is irreducibly complex. It is above physics and chemistry on the epistemological ladder and cannot be subsumed under chemical and physical rules. It harnesses chemistry and physics to its own purposes. As chemist Arthur Robinson, for 15 years a Linus Pauling collaborator, puts it: "Using physics and chemistry to model biology is like using lego blocks to model the World Trade Center." The instrument is simply too crude.

This is, again, what's technically known as "talking out your ass". Chaitin's theory demonstrates no such thing. Chaitin's theory doesn't even come close to discussing anything that could be interpreted as saying anything about biology or chemistry. Chaitin's theory talks about two things: what computing devices are capable of doing; and what the fundamental limits of mathematical reasoning are.

One of the most amazing things about Chaitin's theory is that it shows how any computing device - even something as simple as a Turing machine can do all of the computations necessary to demonstrate the fundamental limits of any mathematical process. It doesn't say "chemistry can't explain biology"; in fact, it's can't say "chemistry can't explain biology".

In fact, in this entire section, he never actually supports anything he says. It's just empty babble. Biology is irreducibly complex. Berlinski is a genius who demonstrates IC in mathematics and biology. Chaitin supports the IC nature of biology. Blah, blah, blah. But in all of this, where he's allegedly talking about how mathematical theories support his claim, he never actually does any math, or even talks about how the theories he's discussing applying to his subject.